Mirror grinding

Yeah this is an interesting area of research - I think the term you're looking for is deconvolution. Here's a document about some of the work done for Hubble in this regard (large PDF): http://www.stsci.edu/hst/HST_overview/documents/Restorationo...

However, my understanding is that you can improve things but you can't "truly" correct it, generally speaking, because the optical aberration causes information to be lost. eg. if point A on your mirror focuses to point A' on the resulting image, and point B on your mirror, due to an aberration, also focuses to A', there's no way to determine from the image which point on the mirror a photon came from.

This is why Hubble eventually needed a hardware fix... from the linked paper: "it is clear that many image restoration methods are highly successful at deriving images that 'look good' from HST data. These restored images may be qualitatively faithful to the true (unknown) image. However, for most astronomical purposes qualitative agreement with reality is not sufficient; we want quantitative agreement as well."

The extraordinary precision (under 0.1 microns) is only possible because the surface is close to a sphere; when grinding two surfaces together uniformly in all directions, the result tends towards a sphere (or a flat shape, which is a sphere of infinite radius). If you had to make an arbitrary shape, things would be very different.

If there's a bump (a hill) on the surface, it tends to grind out more quickly than the rest because it's jutting out and it's more exposed to pressure from the grit. If there's a hole, it remains untouched while the surface around it is being ground down. This way everything tends towards the ideal shape. By carefully doing a uniform rotation of the pieces during grinding, the resulting shape is symmetrical - spherical or flat.

Other shapes are also used in mirrors (revolution surfaces generated by a parabola, hyperbola or ellipse), but they are all basically just small corrections to a sphere (which is a revolution surface generated by a circle).

You start with very rough grit to go faster in the beginning and remove most material. Then you just use finer and finer grit as the surface becomes more and more smooth.

In the final stages you switch to polishing. It's a different process where the tool is not hard (glass) but soft (pitch), and the grit is replaced with microscopic powders (such as iron oxide or cerium oxide) which work not only through physical mechanisms but also via surface chemistry.

Also during polishing you use testing procedures which can show surface errors as small as 0.02 microns. The testing process is steering your polishing techniques; you apply corrections, or choose different polishing strokes to deal with various surface errors. Whereas grinding is mostly automatic (with a few basic checks here and there), during polishing your brain is in the loop, a lot.

Spherometers are only used during the initial stages. Towards the end you switch to optical testing.

Needs the same for lenses. I'm very eager to try optics.

I interned at a great company (https://qedmrf.com/) that engineers magnetorheological fluid and machines for polishing / analyzing optics. I can't imagine doing it by hand. Fascinating stuff.